Spectral detectors have a relatively high cost compared to energy integrating detectors. To reduce cost, a detection system may include a hybrid detector array with both spectral detectors and energy integrating detectors, instead of all spectral detectors. With one approach, the detector array may be populated asymmetrically with spectral detectors. For example, a first set of the detectors may be spectral detectors with the remaining detector being energy integrating detectors. In this example, where the spectral detectors cover a small field of view but not the entire full field of view, full field of view acquisitions will result in a set of truncated spectral projections.
An approach for extending truncated non-spectral projections for an asymmetric profile is discussed in Cho et al. Phys. Med. Biol. 40, 1995, pp. 1863-1883. With this approach, an asymmetric profile is extended with the complementary (or approximately redundant) line integrals measured at the opposite gantry angle. Suitable image quality can be achieved for small cone angles in axial scanning modes. With larger cone angles (e.g., greater than 1.5 degrees) or higher pitch (e.g., greater than 0.8), the 3D image quality of asymmetrically truncated acquisitions is gradually deteriorated. The former is discussed in Schäfer et al., “FBP and BPF reconstruction methods for circular X-ray tomography with off-center detector,” Med. Phys. Vol. 38 (7), S85-S94, 2011, and the latter is discussed in Zamyatin et al., “Helical cone beam CT with an asymmetrical detector,” Med. Phys. 32, 3117-3127 2005. In the spectral case, unfortunately, this problem arises for every spectral channel.